**Learning objectives**

- Work with algebraic and geometric linear combinations
- Work with dot product algebraically and geometrically
- Compute projections of vectors

**Before class**

- Read Hughes-Hallett sections 13.1-3.
- Ponder Hughes-Hallett problems: 13.1: 1, 5, 12, 25, 31, 36, 37, 38, 41; 13.2: 1, 3, 5, 6, 18, 22, 24.; 13.3: 1, 7, 11, 15, 16, 32, 33, 35, 38, 47, (63 for a theoretical challenge).
- Complete HW2 on WeBWork
- Post to Piazza
- Write solutions to problems 12.2: 27; 12.4: 18-20; Review (p680-681): 31-32 to turn in at the beginning of class.

**In class**

- Begin reading On Contour and Slope Lines (1859) by Arthur Cayley
- Activity: vector calculations
- Mathematica for vectors (if time allows)